Scaling Laws and Urban Systems
1st Edition
Published on 20. February 2026
Book
Hardback
352 pages
978-1-78945-228-0 (ISBN)
Description
Interest in scaling laws has grown since the beginning of the 21st century. In both the social sciences and the natural sciences, there is continued astonishment at the increasing inequalities between large and small cities.
While social indicators are often thought of as linear measures, in terms of per capita quantities, economies of scale allow us to take account of sublinear relationships or superlinear relationships (amplifications), achieved according to the size of cities. Given the dual challenge facing cities in terms of ecological transition and technological innovation, it is crucial to inform urban policies about the effects of their size on the qualities of cities.
Scaling Laws and Urban Systems provides an overview of this new knowledge in terms of growth and adaptation capacities, resource extraction or environmental pollution, as well as the sustainability of the living conditions that cities now offer to the majority of the world's population.
While social indicators are often thought of as linear measures, in terms of per capita quantities, economies of scale allow us to take account of sublinear relationships or superlinear relationships (amplifications), achieved according to the size of cities. Given the dual challenge facing cities in terms of ecological transition and technological innovation, it is crucial to inform urban policies about the effects of their size on the qualities of cities.
Scaling Laws and Urban Systems provides an overview of this new knowledge in terms of growth and adaptation capacities, resource extraction or environmental pollution, as well as the sustainability of the living conditions that cities now offer to the majority of the world's population.
More details
Series
Language
English
Place of publication
London
United Kingdom
Target group
Professional and scholarly
Product notice
Laminated cover
Dimensions
Height: 234 mm
Width: 156 mm
Thickness: 21 mm
Weight
673 gr
ISBN-13
978-1-78945-228-0 (9781789452280)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Celine Vacchiani-Marcuzzo | Denise Pumain
Scaling Laws and Urban Systems
E-Book
02/2026
1st Edition
Wiley
€183.99
Available for download
Celine Vacchiani-Marcuzzo | Denise Pumain
Scaling Laws and Urban Systems
E-Book
02/2026
1st Edition
Wiley
€183.99
Available for download
Persons
Celine Vacchiani-Marcuzzo is Geographer and Professor at Universite Paris Cite, France. Her work focuses on the functional and relational aspects of cities (demographic dynamics, economic trajectories, mobility, etc.) from a comparative global perspective.
Denise Pumain is Geographer and Emeritus Professor at Universite Paris 1 Pantheon-Sorbonne, France. As a specialist in urban dynamics, she questions the relevance of transferring models between the natural sciences and social sciences.
Denise Pumain is Geographer and Emeritus Professor at Universite Paris 1 Pantheon-Sorbonne, France. As a specialist in urban dynamics, she questions the relevance of transferring models between the natural sciences and social sciences.
Content
Introduction XIII
Celine VACCHIANI-MARCUZZO and Denise PUMAIN
Part 1 Consolidating the Significance of Urban Scaling Laws 1
Chapter 1 Scaling Laws in Complex Systems Dynamics 3
Denise PUMAIN
1.1 Scaling laws: definition and interpretations 3
1.1.1 Definition of scaling laws 4
1.1.2 Interpretations derived from statistical physics 8
1.1.3 Interpretations incorporating social science theories 9
1.2 A difficult synthesis 13
1.3 Applications of scaling laws 16
1.3.1 Scaling laws and urban morphology 16
1.3.2 Scaling laws and the social and functional typology of cities 18
1.3.3 Scaling laws and zones of influence around cities 19
1.3.4 Scaling laws and degree of development 19
1.3.5 Scaling laws and renormalization 20
1.4 Scaling laws: challenges for urban policy 20
1.4.1 Promoting the equitable distribution of urban services 21
1.4.2 Productivity and city size 21
1.4.3 Large and small cities in the ecological transition 23
1.5 Conclusion 23
1.6 References 25
Chapter 2 Epistemological and Critical Examination of Urban Scaling Laws 35
Cecile TANNIER and Denise PUMAIN
2.1 Introduction 36
2.2 Concept of scale in urban geography 36
2.2.1 Scale as a dimension of geographic objects 37
2.2.2 Scale as a level of spatial organization of societies 40
2.3 Scale invariance of the rank-size distribution of cities and central place systems 46
2.3.1 Distribution of city size: a scaling law like any other? 47
2.3.2 Central place systems and their possible scale invariance 51
2.3.3 Attempts to reconcile the rank-size law of cities and central places theory 53
2.4 Scaling laws: theoretical challenges 55
2.4.1 Transition from transversal to longitudinal and the question of ergodicity 56
2.4.2 Poor integration of scaling laws into urban spatialities and temporalities 59
2.5 Practical issues still unresolved 60
2.5.1 Uncertainties related to the definition and delimitation of cities 60
2.5.2 Uncertainties related to statistical estimation methods 61
2.6 Conclusion 62
2.7 References 64
Chapter 3 Generative Models of Hierarchical Systems of Cities: The Role of Individuals and Firms 75
Cecile TANNIER
3.1 Introduction 75
3.2 Explanatory processes for the hierarchization of systems of cities 77
3.3 Intraurban agglomeration and competition processes explaining interurban hierarchies 79
3.4 Interurban hierarchies explained by the intensity and diversity of intraurban social interactions 80
3.4.1 Settlement scaling theory models 80
3.4.2 Models incorporating the diversity of intraurban economic and social activity 85
3.5 City hierarchies and urban scaling laws resulting from migration or individual interurban interactions 87
3.5.1 Central place models 87
3.5.2 Models of the new economic geography 88
3.5.3 Altmann's (2020) model 93
3.6 Properties of the modeled structures and dynamics 94
3.6.1 Fundamental role of space: an aspect that is more or less present in the models 95
3.6.2 Absence of historical (evolutionary) processes and interactions between levels in models 101
3.7 Conclusion 105
3.8 References 106
Chapter 4 Modeling Interactions Between Cities to Simulate Urban Hierarchies 115
Cecile TANNIER
4.1 Introduction 115
4.2 Three categories of processes at work in the dynamics of systems of cities 117
4.2.1 Spatial interactions between cities 117
4.2.2 Functional specialization of cities and spatial division of labor 118
4.2.3 Hierarchical diffusion of innovations 121
4.2.4 Evolutionary theory of cities 121
4.3 Models 123
4.3.1 So-called "parsimonious" models 123
4.3.2 Models closer to concepts and theories of social sciences 130
4.3.3 More complex models incorporating numerous empirically observed processes 137
4.4 Components of model dynamics 149
4.4.1 Role of space in the models 150
4.4.2 Role of demographic and economic changes 151
4.4.3 Role of the diversity and diversification of functions and activities in cities 153
4.5 Conclusion 155
4.6 References 156
Part 2 Revisiting International Comparison of Urban Systems with Scaling Laws 165
Chapter 5 Urban Functions and Scaling Laws: South Africa, United States, France 167
Celine VACCHIANI-MARCUZZO and Fabien PAULUS
5.1 Scaling laws to the test: a comparative analysis of South Africa, France and the United States 168
5.2 A hybrid system of cities between the new world and developing countries 169
5.3 Scaling laws and industry (economic sectors) 171
5.4 Exploration of occupations 178
5.5 Conclusion 186
5.6 References 186
Chapter 6 Scaling Laws and Integration Dynamics in Cities of the European Union 191
Olivier FINANCE and Denise PUMAIN
6.1 Scaling laws and the diffusion of innovations 193
6.1.1 Urban growth or decline and the diffusion of innovations 193
6.1.2 Scaling laws and stages in the diffusion of innovation waves 199
6.2 Foreign investment flows into European cities 200
6.2.1 Quantitative selectivity of new investments and jobs 201
6.2.2 Variations in scaling laws across city activity sectors 204
6.2.3 Source of investments 206
6.3 Scaling laws and indicators of metropolization 207
6.4 Conclusion 209
6.5 References 209
Chapter 7 The Integration of Cities with Globalization, From 2010 to 2022, Through the Lens of Scaling Laws 215
Celine ROZENBLAT
7.1 Understanding the scaling laws of cities in multinational corporation networks 217
7.1.1 Integration of cities and systems of cities into multisectoral corporation networks 217
7.1.2 Cities and multinational corporations in network 218
7.1.3 Cities in networks of different geographic scopes 218
7.1.4 City ranking and scaling laws 219
7.2 Contribution of scaling laws to understanding the processes of city integration into multinational corporation networks 223
7.3 Reliable database and rigorous methodology 224
7.3.1 Firms' ownership networks 225
7.3.2 Comparable cities defined as large urban regions 226
7.3.3 Data construction by city (LUR) 227
7.3.4 Number of companies as a measure of city size for calculating scaling laws based on enterprise networks 232
7.3.5 City rankings based on company concentration 233
7.4 Scaling laws for cities based on multinational enterprise networks 235
7.4.1 The scaling laws of cities at the global level for multinational enterprise links and their orientations 235
7.4.2 Scaling the laws of cities by the scope of multinational enterprise links at the global level 237
7.4.3 Scaling laws of cities by the scope of multinational enterprise links at the continental level 238
7.4.4 Scaling laws of cities based on their multinational enterprise links by industry 239
7.5 Network properties in urban systems revealed by scaling laws 243
7.5.1 Strength of local links 243
7.5.2 Advantages of diversity 244
7.5.3 Concentration of power 246
7.5.4. Differentiated regimes between the center and the periphery? .. 246
7.5.5 Scaling laws revealing the diffusion of benefits from business concentration in cities 248
7.6 Conclusion 249
7.7 References 250
Part 3 Scaling Laws to Better Characterize Urban Forms 255
Chapter 8 Intra-Urban Radial Scaling Laws 257
Justin DELLOYE, Estelle MENNICKEN, Paul KILGARRIFF, Remi LEMOY and Geoffrey CARUSO
8.1 Introduction 257
8.2 Literature and definitions 259
8.3 Radial approach: concept and empirical measurements 261
8.4 Results 265
8.5 Discussion and conclusion 270
8.6 References 271
Chapter 9 A Method to Define Multiscalar Systems of Cities in France 275
Florent LE NECHET, Benoit CONTI and Sylvestre DUROUDIER
9.1 Introduction 275
9.2 Mobility dynamics and functional interpretations of urbanized spaces 277
9.2.1 Functional areas sometimes lose coherence 277
9.2.2 What frameworks can be used to understand everyday relations between cities? 280
9.2.3 The challenge of multiscalar analysis on the functioning of urban spaces 281
9.3 Proposal for an original method for analyzing the existence of "multiscalar" urban systems 282
9.3.1 Choice of a parametric algorithm for exploratory purposes 282
9.3.2 Description of the first iteration and outputs of the algorithm 283
9.3.3 Two examples of primitive and CUS construction 285
9.3.4 Characterization of the diversity of organizational forms and degrees of multiscalarity in CUSs 287
9.4 Diversity in the spatial organization of urban systems in France 289
9.4.1 National analysis of the role of the ? parameter in the construction of CUSs 289
9.4.2 CUSs to multiscalar consolidated urban systems 294
9.4.3 Test on typology of MCUSs for ? = 4% 295
9.4.4 Analysis of multiscalarity by the morphological organization of the 24 MCUSs (? = 4%) 299
9.4.5 Typology of city multiscalarity 301
9.5 Conclusion 305
9.6 References 306
Conclusion What Role will Scaling Laws Play in the Future of Cities? 311
Celine VACCHIANI-MARCUZZO and Denise PUMAIN
List of Authors 323
Index 325
Celine VACCHIANI-MARCUZZO and Denise PUMAIN
Part 1 Consolidating the Significance of Urban Scaling Laws 1
Chapter 1 Scaling Laws in Complex Systems Dynamics 3
Denise PUMAIN
1.1 Scaling laws: definition and interpretations 3
1.1.1 Definition of scaling laws 4
1.1.2 Interpretations derived from statistical physics 8
1.1.3 Interpretations incorporating social science theories 9
1.2 A difficult synthesis 13
1.3 Applications of scaling laws 16
1.3.1 Scaling laws and urban morphology 16
1.3.2 Scaling laws and the social and functional typology of cities 18
1.3.3 Scaling laws and zones of influence around cities 19
1.3.4 Scaling laws and degree of development 19
1.3.5 Scaling laws and renormalization 20
1.4 Scaling laws: challenges for urban policy 20
1.4.1 Promoting the equitable distribution of urban services 21
1.4.2 Productivity and city size 21
1.4.3 Large and small cities in the ecological transition 23
1.5 Conclusion 23
1.6 References 25
Chapter 2 Epistemological and Critical Examination of Urban Scaling Laws 35
Cecile TANNIER and Denise PUMAIN
2.1 Introduction 36
2.2 Concept of scale in urban geography 36
2.2.1 Scale as a dimension of geographic objects 37
2.2.2 Scale as a level of spatial organization of societies 40
2.3 Scale invariance of the rank-size distribution of cities and central place systems 46
2.3.1 Distribution of city size: a scaling law like any other? 47
2.3.2 Central place systems and their possible scale invariance 51
2.3.3 Attempts to reconcile the rank-size law of cities and central places theory 53
2.4 Scaling laws: theoretical challenges 55
2.4.1 Transition from transversal to longitudinal and the question of ergodicity 56
2.4.2 Poor integration of scaling laws into urban spatialities and temporalities 59
2.5 Practical issues still unresolved 60
2.5.1 Uncertainties related to the definition and delimitation of cities 60
2.5.2 Uncertainties related to statistical estimation methods 61
2.6 Conclusion 62
2.7 References 64
Chapter 3 Generative Models of Hierarchical Systems of Cities: The Role of Individuals and Firms 75
Cecile TANNIER
3.1 Introduction 75
3.2 Explanatory processes for the hierarchization of systems of cities 77
3.3 Intraurban agglomeration and competition processes explaining interurban hierarchies 79
3.4 Interurban hierarchies explained by the intensity and diversity of intraurban social interactions 80
3.4.1 Settlement scaling theory models 80
3.4.2 Models incorporating the diversity of intraurban economic and social activity 85
3.5 City hierarchies and urban scaling laws resulting from migration or individual interurban interactions 87
3.5.1 Central place models 87
3.5.2 Models of the new economic geography 88
3.5.3 Altmann's (2020) model 93
3.6 Properties of the modeled structures and dynamics 94
3.6.1 Fundamental role of space: an aspect that is more or less present in the models 95
3.6.2 Absence of historical (evolutionary) processes and interactions between levels in models 101
3.7 Conclusion 105
3.8 References 106
Chapter 4 Modeling Interactions Between Cities to Simulate Urban Hierarchies 115
Cecile TANNIER
4.1 Introduction 115
4.2 Three categories of processes at work in the dynamics of systems of cities 117
4.2.1 Spatial interactions between cities 117
4.2.2 Functional specialization of cities and spatial division of labor 118
4.2.3 Hierarchical diffusion of innovations 121
4.2.4 Evolutionary theory of cities 121
4.3 Models 123
4.3.1 So-called "parsimonious" models 123
4.3.2 Models closer to concepts and theories of social sciences 130
4.3.3 More complex models incorporating numerous empirically observed processes 137
4.4 Components of model dynamics 149
4.4.1 Role of space in the models 150
4.4.2 Role of demographic and economic changes 151
4.4.3 Role of the diversity and diversification of functions and activities in cities 153
4.5 Conclusion 155
4.6 References 156
Part 2 Revisiting International Comparison of Urban Systems with Scaling Laws 165
Chapter 5 Urban Functions and Scaling Laws: South Africa, United States, France 167
Celine VACCHIANI-MARCUZZO and Fabien PAULUS
5.1 Scaling laws to the test: a comparative analysis of South Africa, France and the United States 168
5.2 A hybrid system of cities between the new world and developing countries 169
5.3 Scaling laws and industry (economic sectors) 171
5.4 Exploration of occupations 178
5.5 Conclusion 186
5.6 References 186
Chapter 6 Scaling Laws and Integration Dynamics in Cities of the European Union 191
Olivier FINANCE and Denise PUMAIN
6.1 Scaling laws and the diffusion of innovations 193
6.1.1 Urban growth or decline and the diffusion of innovations 193
6.1.2 Scaling laws and stages in the diffusion of innovation waves 199
6.2 Foreign investment flows into European cities 200
6.2.1 Quantitative selectivity of new investments and jobs 201
6.2.2 Variations in scaling laws across city activity sectors 204
6.2.3 Source of investments 206
6.3 Scaling laws and indicators of metropolization 207
6.4 Conclusion 209
6.5 References 209
Chapter 7 The Integration of Cities with Globalization, From 2010 to 2022, Through the Lens of Scaling Laws 215
Celine ROZENBLAT
7.1 Understanding the scaling laws of cities in multinational corporation networks 217
7.1.1 Integration of cities and systems of cities into multisectoral corporation networks 217
7.1.2 Cities and multinational corporations in network 218
7.1.3 Cities in networks of different geographic scopes 218
7.1.4 City ranking and scaling laws 219
7.2 Contribution of scaling laws to understanding the processes of city integration into multinational corporation networks 223
7.3 Reliable database and rigorous methodology 224
7.3.1 Firms' ownership networks 225
7.3.2 Comparable cities defined as large urban regions 226
7.3.3 Data construction by city (LUR) 227
7.3.4 Number of companies as a measure of city size for calculating scaling laws based on enterprise networks 232
7.3.5 City rankings based on company concentration 233
7.4 Scaling laws for cities based on multinational enterprise networks 235
7.4.1 The scaling laws of cities at the global level for multinational enterprise links and their orientations 235
7.4.2 Scaling the laws of cities by the scope of multinational enterprise links at the global level 237
7.4.3 Scaling laws of cities by the scope of multinational enterprise links at the continental level 238
7.4.4 Scaling laws of cities based on their multinational enterprise links by industry 239
7.5 Network properties in urban systems revealed by scaling laws 243
7.5.1 Strength of local links 243
7.5.2 Advantages of diversity 244
7.5.3 Concentration of power 246
7.5.4. Differentiated regimes between the center and the periphery? .. 246
7.5.5 Scaling laws revealing the diffusion of benefits from business concentration in cities 248
7.6 Conclusion 249
7.7 References 250
Part 3 Scaling Laws to Better Characterize Urban Forms 255
Chapter 8 Intra-Urban Radial Scaling Laws 257
Justin DELLOYE, Estelle MENNICKEN, Paul KILGARRIFF, Remi LEMOY and Geoffrey CARUSO
8.1 Introduction 257
8.2 Literature and definitions 259
8.3 Radial approach: concept and empirical measurements 261
8.4 Results 265
8.5 Discussion and conclusion 270
8.6 References 271
Chapter 9 A Method to Define Multiscalar Systems of Cities in France 275
Florent LE NECHET, Benoit CONTI and Sylvestre DUROUDIER
9.1 Introduction 275
9.2 Mobility dynamics and functional interpretations of urbanized spaces 277
9.2.1 Functional areas sometimes lose coherence 277
9.2.2 What frameworks can be used to understand everyday relations between cities? 280
9.2.3 The challenge of multiscalar analysis on the functioning of urban spaces 281
9.3 Proposal for an original method for analyzing the existence of "multiscalar" urban systems 282
9.3.1 Choice of a parametric algorithm for exploratory purposes 282
9.3.2 Description of the first iteration and outputs of the algorithm 283
9.3.3 Two examples of primitive and CUS construction 285
9.3.4 Characterization of the diversity of organizational forms and degrees of multiscalarity in CUSs 287
9.4 Diversity in the spatial organization of urban systems in France 289
9.4.1 National analysis of the role of the ? parameter in the construction of CUSs 289
9.4.2 CUSs to multiscalar consolidated urban systems 294
9.4.3 Test on typology of MCUSs for ? = 4% 295
9.4.4 Analysis of multiscalarity by the morphological organization of the 24 MCUSs (? = 4%) 299
9.4.5 Typology of city multiscalarity 301
9.5 Conclusion 305
9.6 References 306
Conclusion What Role will Scaling Laws Play in the Future of Cities? 311
Celine VACCHIANI-MARCUZZO and Denise PUMAIN
List of Authors 323
Index 325